code: def _xyx_decomposition(U, wire, return_global_phase=False):
      r"""Compute the decomposition of a single-qubit matrix :math:`U` in terms
      of elementary operations, as a product of X and Y rotations in the form
      :math:`e^{i\gamma} RX(\phi) RY(\theta) RX(\lambda)`.
  
      Args:
          U (array[complex]): A 2 x 2 unitary matrix.
          wire (Union[Wires, Sequence[int] or int]): The wire on which to apply the operation.
          return_global_phase (bool): Whether to return the global phase ``qml.GlobalPhase(-gamma)``
              as the last element of the returned list of operations.
  
      Returns:
          list[Operation]: Returns a list of gates, an ``RX``, an ``RY`` and another ``RX`` gate,
              which when applied in the order of appearance in the list is equivalent to the unitary
              :math:`U` up to global phase. If `return_global_phase=True`, the global phase is returned
              as the last element of the list.
  
      **Example**
  
      >>> U = np.array([
      ...     [-0.28829348-0.78829734j, 0.30364367+0.45085995j],
      ...     [ 0.53396245-0.10177564j, 0.76279558-0.35024096j]
      ... ])
      >>> decompositions = _xyx_decomposition(U, 0, return_global_phase=True)
      >>> decompositions
      [RX(10.845351366405708, wires=[0]),
       RY(1.3974974118006183, wires=[0]),
       RX(0.45246583660683803, wires=[0]),
       GlobalPhase(1.1759220332464762, wires=[])]
      """
  
      # Small number to add to denominators to avoid division by zero
      EPS = 1e-64
  
      # Choose gamma such that exp(-i*gamma)*U is special unitary (detU==1).
      U = math.expand_dims(U, axis=0) if len(U.shape) == 2 else U
      U_det1, gammas = _convert_to_su2(U, return_global_phase=True)
  
      # Compute \phi, \theta and \lambda after analytically solving for them from
      # U_det1 = expm(1j*\phi*PauliX) expm(1j*\theta*PauliY) expm(1j*\lambda*PauliX)
      lams_plus_phis = math.arctan2(
          -math.imag(U_det1[:, 0, 1]), math.real(U_det1[:, 0, 0]) + EPS
      )
      lams_minus_phis = math.arctan2(
          math.imag(U_det1[:, 0, 0]), -math.real(U_det1[:, 0, 1]) + EPS
      )
      lams = lams_plus_phis + lams_minus_phis
      phis = lams_plus_phis - lams_minus_phis
  
      # The following conditional attempts to avoid 0 / 0 errors. Either the
      # sine is 0 or the cosine, but not both.
      thetas = math.where(
          math.isclose(
              math.sin(lams_plus_phis), math.zeros_like(lams_plus_phis)
          ),
          2
          * math.arccos(
              math.real(U_det1[:, 1, 1])
              / (math.cos(lams_plus_phis) + EPS)
          ),
          2
          * math.arccos(
              -math.imag(U_det1[:, 0, 1])
              / (math.sin(lams_plus_phis) + EPS)
          ),
      )
  
      phis, thetas, lams, gammas = map(
          math.squeeze, [phis, thetas, lams, gammas]
      )
  
      phis = phis % (4 * np.pi)
      thetas = thetas % (4 * np.pi)
      lams = lams % (4 * np.pi)
  
      operations = [
          qml.RX(lams, wire),
          qml.RY(thetas, wire),
          qml.RX(phis, wire),
      ]
      if return_global_phase:
          operations.append(qml.GlobalPhase(-gammas))
  
      return operations
  
file_path: pennylane/pennylane/ops/op_math/decompositions/single_qubit_unitary.py
imports: import numpy
  import pennylane
  from pennylane import math
label_desc: Use image node_id 5 for calling a global function with example usage: _xyx_decomposition(U, wire, return_global_phase) and returns: operations